Supercurrent across a Ferromagnetic Weak Link: How to Fab-

Due to the spatially oscillating induced pair amplitude in SF proximity structures (see section 2.2.2) it is possible to realize negative coupling of two superconductors across a ferromagnetic weak link. In this case of negative coupling, the critical current across the junction is reversed when compared to the normal case giving rise to an inverted CPR (see Figure 2.7). Because they are characterized by an intrinsic phase shift ofπ these junctions are called π-junctions.

2.3. The dc-Josephson Effect 19

IR(V)Cn

p -junction 0- crossover p

Figure 2.8: Dependence of the ICRN product of a SIFS Josephson junc-tion on the F layer thickness d_F [5]. The diluted ferromagnet used in this experiment is P d0.88N i0.12, the temperature is 1.5 K. The zero at dF = 65 ˚A and the reoccurrence for larger layer thicknesses indicates the crossover from zero- toπ-coupling. The d_F corresponding to the two types of ferromagnetic Josephson junctions investigated in this work are indicated by the arrows.

The dependence of theRNIC product on the thickness of the ferromagnetic layer in SIFS junctions has been experimentally investigated by Kontos et al. (see Figure 2.8, [5]).

In the case of ferromagnetic weak links, Eqn. 2.22 which gives the energies of the Andreev bound states n, has to be completed by EEx to account for the additional phase shift the electron-hole pairs acquire due to the presence of the exchange field in the ferromagnet:

∆ϕ= 2n±EEx

~vF

d=±ϕ+ 2 arccosn

∆ + 2πn. (2.23)

The additional term in equation 2.23 shifts the spectral positionsnof the ABS. The sign in front ofEEx corresponds to the two possible spin configurations↑↓ or↓↑for the electron-hole pair. Forϕ= 0 the levels which carry current in opposite directions are again energetically degenerate and compensate each other, so the net current is still zero. For non-zero phase differences however, the degeneracy is lifted and it is possible, depending on EEx and d, that the lowest lying level, which is the most

populated one³, now carries a negative supercurrent, i.e. in the opposite direction when compared to the normal metal case. This means that the supercurrent for these special types of ferromagnetic junctions has changed its sign. The negative sign of the supercurrent results in an inverted CPR

I_S^π =−ICsinϕ=ICsin(ϕ+π), (2.24) where a sinusoidal CPR is assumed.

Figure 2.7 compares the CPRs of a standard (SIS) Josephson junction with a π-junction (according to Eqn. 2.24). The CPR of theπ-junction can be obtained from the standard CPR by a phase shift of π. A π-junction can therefore be considered as a Josephson junction with a built-in phase difference ofϕ=π.

As in the normal metal case, in the diffusive regime, the sharp δ-peaks correspond-ing to the ballistic ABS are broadened and evolve towards a continuous spectral supercurrent density NJ(). The total supercurrent IS is obtained by integrating over the spectral contribution weighted with the thermal occupation of the ABS

IS(T) = 1

By varying the temperature, the spectral contribution to the total supercurrent can be weighted. By employing this mechanism, even a temperature dependent crossover from 0 toπ-junctions can be observed [26, 24]. The condition for utilizing the temperature as a parameter to tune the junction from 0- toπ-coupling is

kBT ≈EEx. (2.26)

Another way to look at the temperature induced crossover from the 0 to the π state in diffusive samples can be found in Eqn. 2.19 [26]. The crossover (0 toπ) of a junction with given layer thickness can be attributed to the temperature dependence of ξF, which sets the length-scale of the oscillation of the induced pair amplitude (see Figure 2.5).

In our samples the diluted ferromagnet Pd0.82Ni0.18 is employed, the corresponding exchange energy is estimated to be of the order of 52 meV. This value corresponds to a temperature of more than 600 K. The condition to have T as an parameter (Eqn. 2.26) is obviously not fulfilled and therefore it is reasonable to assume for

3and determines the direction of the supercurrent

2.3. The dc-Josephson Effect 21

this experiment that the temperature has no influence on the 0- or π-character of the ferromagnetic Josephson junction.

In general, the CPR relation for aπ-junction is predicted to deviate from the simple sinusoidal shape. The CPR for point contacts (SFcFS) and double barrier junctions (SIFIS) for thin diffusive ferromagnetic interlayers was theoretically investigated by Golubov [27].

Experimentally, the exact shape of a CPR is difficult to measure. Bentner has developed a method to directly measure the CPR of mesoscopic SNS junctions [25].

To do so, the junctions are incorporated into contacted superconducting loops and placed on a micro-Hall sensor. The method can be applied for values of the LIC

products smaller than 0.4×Φ0 (see section 2.4.2). IC is the critical current of the junction, L is the inductance of the loop and Φ0 the flux quantum.

It has been predicted, that ferromagnetic Josephson junctions close to the transition point between 0 and π show a CPR with dominating 2ϕ-periodic contribution [28, 29]. Sellier has given an illustrative explanation for the expected 2ϕperiodicity for ballistic junctions[24, 23]. For certain values of the exchange field, the level spacing of the ABS is half of the spacing without exchange field. The reason for this change is the lifted degeneracy of the pairs of ABS with reversed spin configurations. Frolov et al. investigated the CPR of Nb/Cu0.47Ni0.53/Nb junctions which show a temperature induced crossover between the 0- and the π-state. They found a vanishing critical current at the crossover point, and no higher harmonics in the CPR [30]. Sellier et al. investigated the CPR of N b/CuN i/N b junctions by applying a high frequency excitation to the junction and observing the formation of Shapiro steps [23]. They found half-integer Shapiro steps at the crossover temperature which are attributed to the sin 2ϕ dependence of the corresponding CPR.

Besides the ferromagnetic π-junctions described above, there are other ways to pre-pare π-junctions. By contacting the normal layer of a SNS junction and driving a current through it, controllable 0/π-junctions can be realized. Depending on the control current through the normal part of the junction, the energy distribution of the quasiparticles in N is modified and thereby the weighting of the spectral super-current density is modified, giving rise to either 0- or π-junction behavior [31, 4].

In high TC superconductors with d-wave symmetry of the order parameter, grain boundaries are used to create Josephson junctions with negative coupling. The physical mechanism leading to π-junctions in this case is the direction dependence of the order parameter in HTC superconductors [3].

Backhaus et al. found a superfluid analogue to a superconducting π-junction [32].

They observed a metastable superfluid state, where a phase difference ofπ is

main-tained between two weakly coupled macroscopic quantum states which are formed by reservoirs of superfluid ³He.